Can I read A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries on EtoBox?

A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries by Covert, David; Hart, Derrick; Iosevich, Alex; Senger, Steven; Uriarte-Tuero, Ignacio is a scholarly article available to read on EtoBox.

What is A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries about?

We show that if $E \subset \mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field with $q$ elements, and $|E| \geq \rho q^d$, where $ q^{-\frac{1}{2}}\ll \rho \leq 1$, then $E$ contains an isometric copy of at least $c \rho^{d-1} q^{d+1 \choose 2}$ distinct $(d+1)$-point configurations.

Author

Covert, David; Hart, Derrick; Iosevich, Alex; Senger, Steven; Uriarte-Tuero, Ignacio

Published

2010

Language

EN